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# Prime ideals in skew and q-skew polynomial rings / [electronic resource] K.R. Goodearl, E.S. Letzter.

Material type: TextPublisher: Providence, R.I. : American Mathematical Society, 1994Description: 1 online resource (vi, 106 p. : ill.)ISBN: 9781470400989 (online)Subject(s): Ideals (Algebra) | Polynomial rings | Noetherian ringsAdditional physical formats: Prime ideals in skew and q-skew polynomial rings /DDC classification: 510 s | 512/.4 LOC classification: QA3 | .A57 no. 521 | QA247Online resources: Contents
Contents:
1. Introduction 2. Preliminaries for $S$ = $R$[$y; \tau , \delta$] 3. Tau-delta-prime coefficient rings 4. Each prime ideal of $S$ is associated to a unique $\tau$-orbit in spec$R$ 5. Annihilator primes and induced bimodules 6. Prime ideals in quadratic (-1)-skew extensions 7. Prime ideals in $S$ associated to infinite orbits. The general case 8. Prime ideals in $S$ associated to infinite orbits. The $q$-skew case 9. Prime ideals in $S$ associated to finite orbits. The general case 10. Prime ideals in $S$ associated to finite orbits. The $q$-skew case 11. Classification of prime ideals in $q$-skew extensions 12. Irreducible finite dimensional representations of $q$-skew extensions 13. Quantized Weyl algebras 14. Prime factors of coordinate rings of quantum matrices 15. Chains of prime ideals in iterated Ore extensions
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"May 1994, volume 109, number 521 (first of 5 numbers)."

Includes bibliographical references (p. 104-106).

1. Introduction 2. Preliminaries for $S$ = $R$[$y; \tau , \delta$] 3. Tau-delta-prime coefficient rings 4. Each prime ideal of $S$ is associated to a unique $\tau$-orbit in spec$R$ 5. Annihilator primes and induced bimodules 6. Prime ideals in quadratic (-1)-skew extensions 7. Prime ideals in $S$ associated to infinite orbits. The general case 8. Prime ideals in $S$ associated to infinite orbits. The $q$-skew case 9. Prime ideals in $S$ associated to finite orbits. The general case 10. Prime ideals in $S$ associated to finite orbits. The $q$-skew case 11. Classification of prime ideals in $q$-skew extensions 12. Irreducible finite dimensional representations of $q$-skew extensions 13. Quantized Weyl algebras 14. Prime factors of coordinate rings of quantum matrices 15. Chains of prime ideals in iterated Ore extensions

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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